Topological games and strong quasi-continuity

Abstract

Let X be a Baire space, Y be a W-space and Z be a regular topological space. We will show that every KC-function f : X ◊ Y ! Z is strongly quasi-continuous at each point of X ◊ Y. In particular, when X is a Baire space and Y is Corson compact, every KC-function f from X ◊ Y to a Moore space Z is jointly continuous on a dense subset of X ◊Y. We also give a few applications of our results on continuity of group actions.